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J. Found. Comput. Sci."],"published-print":{"date-parts":[[2021,2]]},"abstract":"<jats:p> Let [Formula: see text], where [Formula: see text] is a power of a prime number [Formula: see text] and [Formula: see text]. A triple cyclic code of length [Formula: see text] over [Formula: see text] is a set that can be partitioned into three parts that any cyclic shift of the coordinates of the three parts leaves the code invariant. These codes can be viewed as [Formula: see text]-submodules of [Formula: see text]. In this paper, we study the generator polynomials and the minimum generating sets of this kind of codes. Some optimal or almost optimal linear codes are obtained from this family of codes. We present the relationship between the generators of triple cyclic codes and their duals. As a special class of triple cyclic codes, separable codes over [Formula: see text] are discussed briefly in the end. <\/jats:p>","DOI":"10.1142\/s0129054121500064","type":"journal-article","created":{"date-parts":[[2021,1,4]],"date-time":"2021-01-04T14:16:55Z","timestamp":1609769815000},"page":"115-135","source":"Crossref","is-referenced-by-count":0,"title":["Triple Cyclic Codes Over \ud835\udd3dq + u\ud835\udd3dq"],"prefix":"10.1142","volume":"32","author":[{"given":"Ting","family":"Yao","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Hefei Normal University, Hefei 230601, Anhui, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2845-3568","authenticated-orcid":false,"given":"Shixin","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Mathematics, Hefei University of Technology, Hefei 230601, Anhui, P. R. 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